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Abstract

A general analytic solution for Brillouin distributed sensing in optical fibers with sub-meter spatial resolution is obtained by solving the acoustical-optical coupled wave equations by a perturbation method. The Brillouin interaction of a triad of square pump pulses with a continuous signal is described, covering a wide range of pumping schemes. The model predicts how the acoustic wave, the signal amplitude and the optical gain spectral profile depend upon the pumping scheme. Sub-meter spatial resolution is demonstrated for bright-, dark- and π-shifted interrogating pump pulses, together with disturbing echo effects, and the results compare favorably with experimental data. This analytic solution is an excellent tool not only for optimizing the pumping scheme but also for post-processing the measured data to remove resolution degrading features.

Fig. 4 (a) 3D gain signal diagram in a dark pulse configuration (α = γ = 1, β = 0) as calculated from the full analytic solution of Eq. (A12) for an interacting fiber segment Δz = 1m and T = 1ns. The pulse enters the fiber at t = 10ns. The background Brillouin signal, introduced by the nonzero α or γ has been removed in this 3D diagram by subtraction and the polarity of the spectrum was inverted for clarity. (b) Time-domain plots of the Brillouin gain for different frequency detunings, Eq. (A12) (Here, the background Brillouin signal, mentioned above was not removed and the true polarity of the signal is shown). The observed oscillation frequencies are equal to the detuning values.

Fig. 6 (a) Experimental gain distribution with 0.5ns π−phase pump pulse. (b) Calculated gain distribution for the three concatentated fiber segments used in the experiment, as obtained from the full analytic solution in Eqs. (A10), (A12).

Fig. 9 (a) Experimental gain distribution after filtering by the impulse response of Eq. (8).The scale is linear. (b) Effect of filtering on the frequency distribution along the fiber. The green and blue line corresponds to the original measured data and processed data, respectively.